Background: Prior studies have shown high heritability estimates regarding within-function transmission of neurocognition, both in healthy families and in families with schizophrenia but it remains an open question whether transmission from parents to offspring is function specific and whether the pattern is the same in healthy families and families with schizophrenia or bipolar disorder. We aimed to characterize the transmission of intelligence, processing speed, and verbal working memory functions from both biological parents to their 7-year old offspring in families with parental schizophrenia, bipolar disorder, and population-based control parents. Methods: The population-based cohort consists of 7-year-old children with one parent diagnosed with schizophrenia (n = 186), bipolar disorder (n = 114), and of parents without schizophrenia or bipolar disorder (n = 192). Children and both parents were assessed using identical, age-relevant neurocognitive tests of intelligence, verbal working memory, and processing speed. Results: In multiple regression analyses children's intelligence, verbal working memory, and processing speed scores were significantly associated with the corresponding parental cognitive function score. All associations from parents to offspring across functions were non-significant. No significant parental cognitive function by group interaction was observed. Conclusion: Transmissions of intelligence, processing speed, and verbal working memory from parents to offspring are function specific. The structure of transmission is comparable between families with schizophrenia, families with bipolar disorder and families without these disorders.